"The American soldiers are not fighting by the rivers."
Translation:Az amerikai katonák nem a folyóknál harcolnak.
It is possible. It depends on what you want to negate. Whatever is behind "nem" is the thing being negated. So, not the American soldiers? Not fighting? Not at the rivers?
With "nem a folyóknál", the fighting part is not negated. So, they are probably figthing, but not at the rivers.
With "nem harcolnak", we don't know if they are fighting at all. At the river they are definitely not fighting. Or maybe we are talking specifically about "the peaceful (non-fighting) soldiers" at the rivers.